Question: Solve for $x$ and $y$ using elimination. ${-4x-y = -22}$ ${5x+y = 26}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-4x-y = -22}\thinspace$ to find $y$ ${-4}{(4)}{ - y = -22}$ $-16-y = -22$ $-16{+16} - y = -22{+16}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 4}$ into $\thinspace {5x+y = 26}\thinspace$ and get the same answer for $y$ : ${5}{(4)}{ + y = 26}$ ${y = 6}$